Saturday, July 16, 2016

IoT stands for "Internet of Things": thousands of interconnected devices sharing (sensitive) information and personal data. As many of them are small and embedded (not all: during a summary talk, Florian Böhl pointed out the existence of connected Caterpillars, for instance...these, not these), this directly translates to the need for a careful evaluation of threats due to side-channel attacks.

Benedikt Gierlichs gave a talk about such a crucial aspect of IoT deployment. He introduced the subject by means of possible applications and use-cases (many of which were the main focus of other talks) and by explaining common issues when securing IoT nodes. In particular, he gave a nice "equation" that succinctly describes them.

IoT device = embedded device + network

Although being a quite simplistic representation of nodes, the equation suggests a very interesting peculiarity of IoT devices within the security framework: the possible points of failure are more in number and also more dangerous than usual non-connected devices. As Ingrid Verbauwhede also remarked during the discussion phase, many of those devices are secure by themselves; it's the fact of being part of a network that raises security issues. Indeed network security adds a non-trivial challenge to the already tough work of securing an embedded device. Since such a discussion is prohibitively broad for a workshop talk (in fact spanned the whole workshop), Benedikt outlined three essential components in IoT security. The nodes need:

good cryptography: self-explanatory;

secure interfaces: nodes need to communicate among each other and with hubs, the cloud, servers, smartphones. Each of these exchange of information must happen in a formatted and standardised way, using protocols for instance. In these regards Johan Stokking, co-founder of The Things Network, said in his talk that many devices can't even support the IP protocol because it's too complicated. On top of this, at some point all the data should reach final users, for which secure GUIs and access points are needed;

secure implementations.

Taken the first two points for granted, the remaining of the talk focused on the third one by providing introductory notions on side-channels analysis, in particular an overview on possible attacks (active/passive, invasive/non-invasive). The speaker remarked the number of things that can possibly go wrong even in the situation in which good crypto and secure interfaces are deployed. If such an assumption is dropped, the scenario is even scarier. In the end the moral was that, within the framework of IoT, "protecting against physical attacks is perhaps not the most pressing issue". Arguably the most pressing issue is depicted by the following picture.

The graph is not based on real data, making it somewhat informal (and accordingly, it's been drawn with an informal graphic tool). The x-axis represents the number of IoT devices and the y-axis carries an extremely informal notion of "percentage of security". The story told is that the majority of devices come with almost no security, and a very small part delivers very strong security. A lot of effort has been put to target the left-most part of the graph: developing really secure protocols and algorithms to make the latter, perhaps already reasonably robust, better. What it should be done (more) in order to ship secure products in every house is pushing the overall "percentage of security" up in (almost) all devices.

Thursday, July 7, 2016

On the second day of the Workshop HEAT, Antoine Joux gave an invited talk on the history of cryptanalytic applications of lattice-basis reduction algorithms.

Lattice is a discrete subgroup of $\mathbb{R}^n$. Equivalently, it is a span of integer-linear combinations of $\mathbb{R}$-linearly independent vectors in $\mathbb{R}^n$. Finding a short basis in $\mathbb{R}^2$ is relatively easy and Gauss' lattice-basis reduction algorithm is effective for this purpose. As the speaker emphasised, things become more complicated when we move to higher dimensions. He then went on to discuss the details of the famous LLL algorithm, invented by Lenstra, Lenstra and Lovász in 1982, for lattice-basis reduction in arbitrary dimensions. LLL is a polynomial-time algorithm but returns a short vector within an exponential approximation factor of the length of the shortest vector in the lattice. This algorithm, which performs well in practice, may be viewed as a combination of the Gauss lattice reduction and the Gram-Schmidt orthogonalisation methods.

An early application of lattice-basis reduction is the cryptanalysis of knapsack-based cryptosystems. The knapsack problem, a.k.a. the subset-sum problem, is given integers $a_1, \ldots, a_n$, and $S$, find $\epsilon_1,\ldots,\epsilon_n \in \{0,1\}$ such that

\[S = \overset{n}{\underset{i=1}{\sum}} \epsilon_i \cdot a_ i.\]

This problem is NP-hard though some cases are easy, and it served as a basis for cryptosystems such as Merkle-Hellman cryptosystem. The basic idea is to hide an easy knapsack in a hard-looking one. However, at CRYPTO 1982, Shamir broke this cryptosystem using lattice-basis reduction. This attacks works for super-increasing knapsacks, where we have $a_i > \sum_{j=1}^{i-1} a_j$. Other works starting with that of Lagarias-Odlyzko in 1985 lead to improved attacks on low-density knapsacks.

The speaker also briefly spoke about the application of lattie-basis reduction to the problems of

reconstructing small linear dependencies: let $(x_1,\ldots,x_n)$ be a sequence of real numbers, we need to find small coefficients $v_i$ such that $\sum v_i\cdot x_i =0$,

constructing polynomials for use in the Number Field Sieve for solving the Discrete Logarithm Problem, and

Tuesday, July 5, 2016

The second HEAT workshop on Fully Homomorphic Encryption (otherwise known as WHEAT) kicked off this morning in (disappointingly cloudy) Paris.

The first talk of the day was Martin Albrecht's invited talk on solving short secret LWE instances. This is joint work with Rachel Player and Sam Scott. He provided a clear summary of the state of the art in terms of algorithms available and thus set the grounds for the rest of the day. Attacks using parameter choices inspired by HElib and the LP model were discussed and where possible, estimate running times were provided. A partial conclusion was the latter should not be assumed. For a more detailed read, see https://eprint.iacr.org/2015/046.pdf.

Also discussed was RLWE security in the FHE case, a talk given by Guillaume Bonnoron. This is joint work with Caroline Fontaine. They present an attack on specific FHE parameter choices and use the FV scheme for the reason that they wish to avoid doing a Modulus Switch Operation (see for example https://eprint.iacr.org/2015/889.pdf for a description). The conclusion of this talk is that their attack does work, but FHE and RLWE are not broken, because it does not scale up. A bigger parameter $n$ leads to bigger errors. Whilst they took one day to complete the attack versus a previous 3.5 days (https://eprint.iacr.org/2015/176.pdf), this talk's final conclusion was that more cryptanalysis is needed.

The second invited talk in the afternoon was Leo Ducas', joint work with Martin Albrecht and Shi Bai. This discussed the subfield lattice attack on "over stretched NTRU assumptions"; for the full technical read, see https://eprint.iacr.org/2016/127.pdf. This attack is based on using a subfield of the field we are working in - they assume the latter is a power of two cyclotomic, but claim it can be done using any field which is Galois. We map down our RLWE instances using the (partial) norm map in order to solve a (hopefully) easier problem in the subfield. Given the right conditions, we can then map the solution we find back up and recover a short enough solution to carry through with the attack. The practicality grows with the modulus $q$, hence the "over stretched" condition. Although this does not seem (yet?) to affect the NTRU schemes used in practice, this talk's conclusion was to drop the NTRU assumption altogether.